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Mechanical behavior improvement of open-pore copper foams synthesized through space holder technique
Materials and Design 49 (2013) 834–841
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Mechanical behavior improvement of open-pore copper foams synthesized through space holder technique A.M. Parvanian ⇑, M. Panjepour Department of Materials Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran
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Article history: Received 3 December 2012 Accepted 29 January 2013 Available online 20 February 2013 Keywords: Open cell metallic foam Lost carbonate sintering Mechanical strength Design of experiments Response surface methodology
a b s t r a c t The use of modern porous materials in different engineering applications necessitates more concentration on open interconnected metallic foams with acceptable mechanical behavior. In this study, openpore copper foams of different porosity percentages with various pore sizes were synthesized through lost carbonate sintering method and then characterized. The effect of copper mechanical pre-activation treatment on flexural strength of the foams was also investigated. The results showed that foams produced by mechanically activated copper powder (350 rpm, 5 h, BPP of 5) have a higher structural integrity, thus enjoying more enhanced mechanical strength relative to specimens without any pre-activation. This may be due to stronger struts mainly resulting from efficient filling of matrix powder between space holder particles. The response surface methodology was also used to examine the effects of carbonate volume percentage and its particle size on the flexural behavior of mechanically optimized foams. Based on the analysis of variances, it was found that the mechanical properties of the foams would improve as a consequence of porosity reduction, while similar relation also exists as average pore sizes decrease. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Porous metallic materials generally known as metal foams have been of increasing interest during recent years due to their unique properties such as high specific strength, heat, electrical conductivity. Based on its openings and connectivity, porosity in metal foams could be divided into closed and open pores. The metallic foams with open interconnected pores are multi-functional, especially for mass and heat transfer applications. For instance, open-pore metallic foams with cell sizes of sub-millimeter were successfully used in fuel cell systems [1,2]. In spite of the numerous methods available for the production of porous metals, only a few are capable of creating open cell foams. In this case, powder metallurgical (PM) processes based on using space holder agent were successfully employed to produce partially open-pore metal foams. Wide range of materials like organic [3,4], inorganic [5] and ceramic particles [6] or even metallic hollow spheres [7] could be used as spacer agent in PM space holder techniques. However, these processes were found to be imperfect. In most cases the mechanical behavior of PM foam products was not very competitive with other more expensive counterparts produced by casting and infiltration methods which are technically very
⇑ Corresponding author. Tel.: +98 311 3912750; fax: +98 311 391 2752. E-mail addresses: [email protected] (A.M. Parvanian), [email protected] (M. Panjepour). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.01.077
expensive and almost suitable for closed-pore foams [8]. In recent years, some research activities were carried out to overcome these shortcomings e.g. by optimization of some process parameters [9,10] or by the introduction of secondary small pores into cell walls [11]. Other activities in this field are devoted to find the relationship between the foam mechanical behavior and some pore network features. Examples include research works done by Wen et al. [12] and similarly by Jiang et al. [13] on the effect of pore size and relative density of some metallic foams on their compressive properties. Others like Goodall et al. [14] have investigated the variation in mechanical response of metallic foams respect to the tortuosity and pore morphology. On the other hand, lots of these cellular structural properties could be controlled by selecting proper parameters in PM method [15,16]. For instance, foam’s porosity percentage, e, and also its average pore diameter, dpore, are closely dependent on the volume percentage of sacrificial space holding material, fc, and its particle size, dc, respectively [17]. So, enhancing the mechanical strength of PM porous products is guaranteed by proper adjusting of process factors. However, it seems that more efforts should be made to improve open cellular metallic foams’ mechanical behavior for high technological applications. The goal of this research work is to manufacture open-pore copper foams by the space holder technique and to understand the effect of matrix powder mechanical pre-activation treatment on the mechanical response of foam products. In the following, the dependency of these metal foams’ mechanical behavior on some intrinsic
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parameters will be studied through a series of designed experiments. 2. Experimental procedure 2.1. Foam synthesis The lost carbonate sintering method patented by Zhao et al. [18] has been used in this research to produce open-cell copper foams. The 99.9% pure commercial copper powder with a particle size of <45 lm was used as matrix phase. As a space holder agent, commercial potassium carbonate powder was sieved into three different powder sizes of 595–841 lm (20 + 30), 420–595 lm (30 + 40), and 297–420 lm (40 + 50) with their corresponding ASTM mesh numbers shown in parentheses. For convenience, this classification was labeled, based on the high levels of ASTM mesh numbers, into 30, 40 and 50, respectively. Different steps of synthesis process are schematically illustrated in Fig. 1. First, the Cu and K2CO3 powders were blended in proper portions with ethanol as binder. In the next step, 30 30 mm2 green compacts were formed under 250 MPa hydraulic pressures. The solid state sintering of the foams was carried out under inert atmosphere preheated to 850 °C for 4 h. Subsequently, space holding carbonate material was thermally decomposed at 1000 °C (2 h). Finally, the specimens were cooled naturally at ambient temperature. In the first step of the experiment, the effect of copper powder pre-activation treatment on the mechanical strength of the foams was investigated. The copper powder was mechanically activated in a planetary ball mill at 350 rpm for about 5 h with balls per powder (BPP) ratio of 5. Fig. 2 depicts the scanning electron microscopy images of pure (Fig. 2a) and mechanically activated (Fig. 2b) copper powders. Afterwards, foams with 70 and 80 vol.% of K2CO3 classified as 50 mesh number, were synthesized and their three-point bending strength, as a criterion of samples’ mechanical behavior, was characterized according to ASTM: E 290. This test was selected as a criterion for the evaluation of mechanical behavior, because the sample in this situation simultaneously encountered compression and tension forces. While selecting proper values for fc and dc through space holder technique could satisfy the manufacturer with the desired e and dpore, the effects of fc and dc factors on flexural properties of foams made of mechanically activated copper were also tried. It was performed by the design of experiments (DOEs) based on central composite design (CCD). First, some screening experiments were performed to choose the appropriate levels to study the factors. For instance, the degree of carbonate loss depended on the sample thickness and decomposition time of specimens with K2CO3 particle sizes smaller than 125 lm [15] which seemed to be reasonable for particles coarser than 250 lm. The collapse of the green bodies with carbonate powders coarser than 800 lm, on the other hand, was more probable [19]. So, the K2CO3 particle size of about 300–800 lm was chosen. Practically, porosities less than about
Fig. 2. SEM micrographs of (a) pure copper powder and (b) after mechanical preactivation treatment (350 rpm, 5 h, BPP of 5).
0.55 resulted in very densely closed foams, while those more than about 0.85 could not provide an acceptable mechanical strength [19]. Therefore, the range of 60–80 porosity percentages was also selected. Finally, fc factor at 60, 70 and 80 levels, and dc with three levels of 30, 40 and 50 were selected for these serial experiments. In spite of full factorial experiments, it is possible to understand the governing relation between the response and the factors more efficiently by the analysis of variances (ANOVA) in CCD resulting from a limited number of experiments. Consequently, the response surface methodology (RSM) could be applied to evaluate the relevance of the mechanical response to selected factors in a wider range. The CCD experimental runs consisting of 22 factorial, four axial, and five center points are shown schematically in Fig. 3. They are also listed in detail in Table 1. For each factor, three levels of 1, 0 and +1 based on their value are coded i.e. low, intermediate, and high, respectively. It is noteworthy to mention that the randomized run order of the experiments considered in this study was to reduce the effects of the factors that were not included; particularly, those effects which were time-dependent. The specimen codes in Table 1 consist of a number after M in which the first two digits demonstrate fc and the second two digits state its corresponding abridged particle size. For the center point runs, the standard order of the specimens is followed at the end of the code. The design and analysis of CCD runs were done by MinitabÒ release 14 software package [15]. 2.2. Characterization The Universal Hounsfield H50KS setup with the loading speed of 1 mm/min was employed in all of the mechanical tests. The flexural strength, rf, of foams could be calculated through Eq. (1) as follows:
Fig. 1. Schematic of lost carbonate sintering process used in this study.
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Fig. 3. Schematic of CCD experimental runs to study the effects of fc and dc on the strength of foams made from mechanically activated copper.
Table 1 Full details of 13 CCD experimental runs.
3. Results and discussion
Standard order
Run order
Specimen code
fc Coded level
dc Coded level
Factorial 1 2 3 4
12 7 4 8
M6030 M6050 M8030 M8050
1 1 +1 +1
1 +1 1 +1
Axial 5 6 7 8
1 2 11 5
M7030 M7050 M6040 M8040
0 0 1 +1
1 +1 0 0
Central 9 10 11 12 13
6 10 9 13 3
M7040-09 M7040-10 M7040-11 M7040-12 M7040-13
0 0 0 0 0
0 0 0 0 0
rf ¼ 3FL=ð2bd2 Þ
3.1. The effect of mechanical pre-activation treatment This section presents the experimental results for the evaluation of foams’ mechanical behavior as a consequence of copper powder pre-activation treatment. The flexural properties of foams produced by powders with and without mechanical activation pretreatment are compared in Fig. 4 as stress–strain curves of samples in two different densities. The dashed lines are related to the foams with no mechanical activation of copper powder (C7050, C8050) and the continuous ones are for samples made of mechanically activated copper (AC7050, AC8050). Similarly, for all of these curves, initial stress grows versus strain with a steep slope. This
ð1Þ
where F is the maximum load before cracking, b is the sample width and d its thickness. The plunge diameter was 3 mm and the span between the two lower supports, L, was selected as 18.5 mm. The flexural modulus of the samples, Ef, can be also calculated using the following equation: 3
Ef ¼ ðmL3 Þ=ð4bd Þ
ð2Þ
where the constant m in the recent equation is the slope of the tangent to the initial straight-line portion of the load–deflection curve. Afterwards, the bulk density of specimens, q, was measured based on ASTM: C20 according to the following equation:
q ¼ W 1 =W 2
ð3Þ
where W1 is dry weight and W2 is the suspended weight of porous specimen in water. Knowing the solid copper matrix theoretical density, qs, was assumed to be 8.94 g cm3 [20], making it possible to calculate e of foam product by the following equation:
e ¼ ð1 q=qs Þ 100
ð4Þ
Scanning Electron Microscopy (SEM) was also used by means of Seron Technology model 550i setup to study the microstructural features of copper foams fracture surfaces. Image analysis of SEM micrographs was performed in OrionÒ image analysis software package.
Fig. 4. Stress–strain curves of foams produced from as received (dashed) and mechanically activated (continuous) copper powder in two different densities.
Table 2 Measurements of mechanical properties and some internal features of samples with and without mechanical pre-activation of copper powder. Sample code
rf (MPa)
Wb
qf (g cm3)
e (%)
rf/qf (MPa/g cm3)
C7050 C8050 AC7050 AC8050
7.2 2.7 22.8 6.6
225.25 105.52 855.61 163.29
2.8 1.9 3.1 2.1
68.7 78.7 65.7 77.2
2.6 1.4 7.4 3.1
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increment continues with a gentle slope. As soon as the flexural force becomes more than the tolerance of porous bodies, the first crack appears and load starts to decrease rapidly as the crack propagates. The mechanical properties of foam samples, rf and bending energy absorption capacity, Wb, i.e. proportional to the underneath area of load–displacement curves in the three-point bending test, are listed in Table 2. Some other characteristics of the porous structures like their q, e and strength to density ratios (rf/qf) are also summarized in this table. The results of C7050 and C8050 are in good agreement with a similar work in the same condition for foam synthesis by spherical copper powder [15]. As summarized in this table and graphically depicted in Fig. 4, the mechanical re-
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sponse of foams has enhanced as a result of mechanical pre-activation of matrix copper powder. This is on average two orders of magnitudes for flexural strength, bending energy absorption capacity and specific flexural strength data. This increment in mechanical load bearing capability of open-pore structures could assure their most modern applications. This phenomenon is more evident for samples with higher densities i.e. those with lower K2CO3 volume percentage. Fig. 5 illustrates microstructure of the samples’ fracture surfaces. In this figure, each specimen cell-wall structure is also depicted in higher magnifications. Generally speaking, the mechanical deformation of porous bodies with porosities more than 0.3 mainly occurs as a consequence of distortion in cell-wall
Fig. 5. SEM micrographs from fracture surfaces of copper foam samples; (a and e) C7050, (b and f) C8050, (c and g) AC7050, and (d and h) AC8050.
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Fig. 6. Schematic illustration of strut strengthening mechanism due to the matrix powder mechanical pre-activation in porous media synthesis process.
regions [21]. Therefore, cell wall thickness would severely influence the mechanical strength of these kinds of materials. The mechanical pre-activation of raw copper powder leads to irregular flake shapes with much more contact areas in which some agglomerations could also occur (Fig. 2). Naturally, the flake morphologies have higher compressibility and sintering efficiency than other particle shapes [22]. Fig. 6 schematically shows the porous media synthesis process. This morphological change can severely reduce the number of micropores during compaction step, shown as white arrows in Fig. 5e and f, resulting in stronger mechanical bonding between matrix particles. Thus, merging of flake copper particles eventuates in a more efficient solid state sintering process. This could form denser struts with more continuity of the solid skeleton or stronger necks to withstand mechanical stresses several orders of magnitudes. The denser the foam sample, the more efficient the strut strengthening is.
Fig. 7. Main effects of fc and dc on the porosity (top) and average pore size (bottom) of copper foams.
Table 4 ANOVA of full quadratic regression model for flexural strength data. Source
d.f.
Seq. SS
Adj. SS
Adj. MS
f
p
fc dc fc fc dc dc fc dc Error Total
1 1 1 1 1 7 12
1008.29 9.33 0.00 0.02 8.97 148.40 1175.00
1008.29 9.33 0.00 0.02 8.97 148.40
1008.29 9.33 0.00 0.02 8.97 21.20
47.56 0.44 0.00 0.00 0.42
0.000 0.528 0.999 0.979 0.536
3.2. Response surface methodology (RSM) The experimental results of CCD runs investigating the effects of some pore network features on mechanical response of foams produced from mechanically activated copper powder are discussed in
this section. Table 3 summarizes measurements of these foams’ internal features and also their mechanical strength data. The ANOVA as a reliable tool could be used to understand the meaningful
Table 3 Measurements of foams’ internal features and their mechanical properties. Standard order
Specimen code
qf (g cm3)
e (%)
dpore (lm)
rf (MPa)
rf/qf (MPa cm3 g1)
1 2 3 4 5 6 7 8 9 10 11 12 13
M6030 M6050 M8030 M8050 M7030 M7050 M6040 M8040 M7040-09 M7040-10 M7040-11 M7040-12 M7040-13
3.3 3.2 2.1 2 2.5 3.1 3.4 2 2.5 2.8 2.8 3.1 2.7
62.9 63.8 76.5 77.2 72.3 65.7 62.3 77.3 71.5 69.1 68.5 65.3 69.6
619 ± 22 401 ± 17 622 ± 9 384 ± 21 623 ± 23 380 ± 23 529 ± 23 509 ± 10 542 ± 11 500 ± 15 477 ± 23 529 ± 8 453 ± 10
26.93 33.16 6.57 6.81 23.85 24.86 39.97 8.9 15.48 22.84 18.55 16.8 20.52
8.2 10.4 3.1 3.4 9.5 8.0 11.8 4.5 6.2 8.2 6.6 5.4 7.6
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Fig. 8. Residual plots for flexural strength statistical analysis as (a) normal probability distribution; (b) histogram; (c) residuals versus fits; and (d) residuals versus order.
Table 5 Fitted regression models on flexural strength data with each R square values. Model
R2
R2adj:
R2predict:
Linear Linear + squares Linear + interaction Full quadratic
86.61 86.61 87.37 87.37
83.93 79.91 83.16 78.35
75.73 55.22 66.23 23.42
Table 7 Linear regression model coefficients. Term
Coefficient
S.E. Coef.
t Value
p Value
Constant fc dc
20.403 12.963 1.249
1.100 1.620 1.620
18.453 8.004 0.770
0.000 0.000 0.459
S = 3.96722, R2 = 86.61%, R2adj: ¼ 83:93%, R2predict: ¼ 75:73.
Table 6 ANOVA of linear regression model fitted on flexural strength data. Source
DF
Seq. SS
Adj. SS
Adj. MS
f Value
p Value
fc dc Residual error Total
1 1 10 12
1008.29 9.33 157.39 1175.00
1008.29 9.33 157.39
1008.29 9.33 15.74
64.06 0.59
0.000 0.459
effects of synthesis parameters i.e. fc and dc on these data. Indeed, ANOVA was applied to test the null hypothesis with respect to the data acquired during designed experimentations. Through null hypothesis it is assumed that there is no difference in treatment means (H0:l1 = l1 = = la). The ANOVA results are plotted in Fig. 7 as the main effects of fc and dc on some geometrical features of foams, i.e. their e and dpore. By comparing the slopes of the lines, one can compare the relative magnitudes of the effects of each factor. Apparently, fc could induce the main influential effect on samples’ e and dc as well as on foams’ dpore, while the effect of the complementary factor in each case is negligible; regarding the fact that increasing ASTM mesh number
Fig. 9. The RSM of flexural strength values vs. fc and dc.
of carbonate powder, which means the decrement of dc, equally decreases samples’ dpore. Actually, these analyses can properly de-
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Fig. 10. The contour plot of flexural strength values vs. fc and dc.
scribe the dependency of e and dpore of the porous structures produced via space holder techniques on the volume percentage, fc, and particle size, dc, of sacrificial agent, respectively. This is why this method could be used for the synthesis of porous structures with desired e and dpore. In the following, regression statistical analysis of flexural strength data (Table 3) is performed and the results are presented as ANOVA calculations with full quadratic terms of fc and dc in Table 4. It is noteworthy to mention that all ANOVA calculations in this study have been done using coded units of 1, 0 and +1 for low, intermediate and high levels for each factor, respectively. The corresponding residual plots are also illustrated in Fig. 8. The normality of residuals could be understood from the straight line distribution as shown in Fig. 8a. The bell-shaped histogram plot in Fig. 8b also confirms the error normality assumption. The scattered distribution of dots with no structure above and below the abscissa (fitted values) in Fig. 8c and d proves both the error independency and variance constancy [23]. Generally, regression coefficients with p values less than the confidence interval of 0.05 would have more significant changes on the response. As seen from Table 4, term fc that was proved before as the main controlling factor of foams’ e, is the most significant coefficient in this regression model. In any case, other models including linearity with and without interaction or square terms of factors should be checked to find the best fitted model. The fitted R2 values of other regression analyses are listed in Table 5.
According to Table 5, the values of R2 and R2adj: indicate the goodness of the model to fit the data, while R2predict: shows how well the model predicts responses to new observations. Actually, the recent parameter can prevent over-fitting of the model and could be more useful than R2adj: to compare the models, because it is calculated by the use of observations which are not included in the model estimation [24]. As this table suggests, linear regression model is the best with the highest R2adj: and R2predict: values to predict foams’ flexural response. The R2 value also indicates that the predictors explain 86.61% of the variances for flexural strengths in this regression model. The linear regression model can be the most reliable to predict the flexural strength data. The ANOVA results for this model are also summarized in Table 6. The coefficients of factors and factor effects of this model, analyzed by coded units, are also listed in Table 7. Regularly, for a confidence level of 95%, dc does not show any effect as much significant as fc, but as a main factor it may be helpful to study it more in detail by means of response surface methodology. Fig. 9 depicts the RSM of flexural strengths as a linear function of fc and dc. The projected contours on the factor’s plane, as shown in Fig. 10, suggests a minor improvement of copper foams’ mechanical behavior with a decrement of fc and an increment of dc which means a decrease in e and dpore. In this regard, the effect of e on the mechanical behavior of foams seems to be in good agreement with other similar works [13,16,21,25,26]. The power relationship between Young’s modulus of a cellular structure, E, and its relative density, q/qs, reported by Gibson and Ashby [21], may be the most applicable one known as GA model (Eq. (5)).
E=Es ¼ Cðq=qs Þ2 ¼ Cð1 eÞ2
ð5Þ
where Es is Young’s modulus of solid matrix and is assumed to be around 170 GPa for copper matrix; C and n are also geometric constants of proportionality. The value of C was suggested to be within the range of 0.1–4 for idealized open cellular structures under compression forces [21]. In the case of porous samples’ flexural modulus, an equation similar to Eq. (5) could be also assumed [27]. The relative flexural modulus of synthesized copper foams, Ef/Es, versus their densities, q/qs, are plotted in Fig. 11. A power regression equation with C = 0.0173 and n 1.9 was also fitted on this curve with R2 80%. Through pressurizing the powder mixture in LCS process, the space holder particles tend to glide on each other and rearrange preferentially along their elongated sides. This could result in a nonisotropic foam with irregular pore structure. As cited before, Eq. (5)
Fig. 11. Relative flexural modulus vs. relative density of copper foam products.
A.M. Parvanian, M. Panjepour / Materials and Design 49 (2013) 834–841
has been introduced for open-pore metallic foams with a regular pattern of pore structure. So, the minor differences between the fitted equation and GA model may refer to the irregularity or nonhomogeneity of pore structure in copper foam products which may results in cell walls even without any contribution to load bearing. Despite the effects of e or relative density on mechanical properties of copper foams, there are some contradictories associated with their dpore which could be controlled closely by dc. Using a simple model for porous metallic foams failure, Gibson and Ashby [21] found no relation between the collapse stress and pore size. Tao et al. [16] reported higher rf and Wb for porous copper samples produced by LCS with coarser carbonate powder. The spacious interstices between larger K2CO3 particles surrounded by the spherical Cu powder, were stated as the main reason for stronger cell wall structure. However, it was also suggested that this size difference effect should be insignificant for K2CO3–copper particle size ratio of greater than five. Jiang et al. [13] also discovered an increase in compressive stress–strain curves of Al foams due to an increment of carbamide sacrificial particles ranging from 0.45 to 2 mm. As another finding, improvement of reproducibility and predictability of compressive properties and control precision of relative density due to dpore increase were noticed in this work and also in [25]. On the other hand, some researchers reported higher mechanical strength for the porous metallic materials with smaller dpore [12,28]. Changes in aspect ratio of the cell wall thickness against its edge length has been stated as one of the most promising reasons for this phenomenon [28]. Anyway, the mechanical pre-activation treatment of copper powder performed in this study led to the finer flake particles which could form a thin cover around K2CO3 spheres which completes the filling of interstitial spaces between space holder particles and can minimize the defects in cell wall region mentioned in [16]. In other words, as discussed before, more efficient sintering process could be achieved due to this change in matrix powder morphology. These enhancements would form ligaments with better structural integrity and with stronger cell walls to withstand mechanical loadings. Somehow, as illustrated in Figs. 9 and 10, this strength improvement is more significant for the foams with smaller dpore. In fact, pore size decrement as a consequence of increasing carbonate ASTM mesh number in this study, may increase the density of stronger ligaments i.e. the number of struts in a definite volume, which might improve porous structure mechanical response. 4. Conclusions Synthesis and development of open-pore copper foams through LCS method were investigated in this study. The results show that space holder techniques like LCS could accurately control the e and dpore of the final foam products. It was found that mechanical preactivation of copper powder, and thus changing its morphology could enhance the structural integrity of foams and thus their mechanical strength at least two orders of magnitudes. This was noticeable in foams with higher densities. A series of designed experimental runs on these mechanically enhanced foams also revealed that increasing carbonate volume percentage and equally increasing e could rigorously influence flexural strength of specimens through a power relation similar to GA model. It was also found that decreasing dpore resulted in better mechanical responses, which is mainly due to more integrated struts in a definite volume of the foams with smaller dpore produced by mechanically activated copper powder. However, more thorough study may be needed to investigate this effect in a wider range of particle sizes.
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Acknowledgments The authors would like to gratefully acknowledge the authorities of Iran Renewable Energy Organization (SUNA) for providing the financial support for this research. We would also like to thank Dr. Aloisio Nelmo Klein and Irene Cristina Magnabosco Mocellin for their constructive comments. References [1] Chen R, Zhao TS. Porous current collectors for passive direct methanol fuel cells. Electrochim Acta 2007;52:4317–24. [2] Bidault F, Brett DJL, Middletonc PH, Absond N, Brandona NP. A new application for nickel foam in alkaline fuel cells. Int J Hydrogen Energy 2009;34:6799–808. [3] Alizadeh M, Aliabadi MM. Compressive properties and energy absorption behavior of Al–Al2O3 composite foam synthesized by space-holder technique. Mater Des 2012;35:419–24. [4] Jiang B, Zhao NQ, Shi CS, Du XW, Li JJ, Man HC. A novel method for making open cell aluminum foams by powder sintering process. Mater Lett 2005;59:3333–6. [5] Hassani A, Habibolahzadeh A, Bafti H. Production of graded aluminum foams via powder space holder technique. Mater Des 2012;40:510–5. [6] Mondal DP, Majumder JD, Jha N, Badkul A, Das S, Patel A, et al. Titaniumcenosphere syntactic foam made through powder metallurgy route. Mater Des 2012;34:82–9. [7] Neville BP, Rabiei A. Composite metal foams processed through powder metallurgy. Mater Des 2008;29:388–96. [8] Banhart J. Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci 2001;46:559–632. [9] Surace R, Filippis LACD, Ludovico AD, Boghetich G. Influence of processing parameters on aluminium foam produced by space holder technique. Mater Des 2009;30:1878–85. [10] Ahmed YMZ, Riad MI, Sayed AS, Ahlam MK, Shalabi MEH. Correlation between factors controlling preparation of porous copper via sintering technique using experimental design. Powder Technol 2007;175:48–54. [11] Han F, Cheng H, Wang J, Wang Q. Effect of pore combination on the mechanical properties of an open cell aluminum foam. Scripta Mater 2004;50:13–7. [12] Wen CE, Yamada Y, Shimojima K, Chino Y, Hosokawa H, Mabuchi M. Compressibility of porous magnesium foam: dependency on porosity and pore size. Mater Lett 2004;58:357–60. [13] Jiang B, Wang Z, Zhao N. Effect of pore size and relative density on the mechanical properties of open cell aluminum foams. Scripta Mater 2007;56:169–72. [14] Goodall R, Marmottant A, Salvo L, Mortensen A. Spherical pore replicated microcellular aluminium: processing and influence on properties. Mater Sci Eng A 2007;465:124–35. [15] Zhang YP, Zhao YY. Fabrication of high melting-point porous metals by lost carbonate sintering process via decomposition route. Proc Inst Mech Eng Part B – J Eng Manuf 2008;222:267–71. [16] Tao XF, Zhang LP, Zhao YY. Mechanical response of porous copper manufactured by lost carbonate sintering process. Mater Sci Forum 2007;539–543:1863–7. [17] Bafti H, Habibolahzadeh A. Production of aluminum foam by spherical carbamide space holder technique-processing parameters. Mater Des 2010;31:4122–9. [18] Zhao YY, Fung T, Zhang LP, Zhang FL. Lost carbonate sintering process for manufacturing metal foams. Scripta Mater 2005;52:295–8. [19] Parvanian AM, Panjepour M, Aryanpour G. Development of porous metallic materials for application in fuel cells. Isfahan: Isfahan University of Technology; 2011 [in Persian]. [20] www.matweb.com. [21] Gibson LJ, Ashby MF. Cellular solids: structure and properties. Cambridge: Cambridge University Press; 1997. [22] Upadhyaya GS. Powder metallurgy technology. Cambridge, England: Cambridge International Science Publishing; 2002. [23] Montgomery DC. Design and analysis of experiments. John Wiley & Sons Inc.; 2000. [24] Minitab statistical software help. Release 14 ed. [25] Michailidis N, Stergioudi F, Tsouknidas A, Pavlidou E. Compressive response of Al-foams produced via a powder sintering process based on a leachable spaceholder material. Mater Sci Eng A 2011;528:1662–7. [26] El-Hadek MA, Kaytbay S. Mechanical and physical characterization of copper foam. Int J Mech Mater Des 2008;4:63–9. [27] Ashby M, Evans A, Fleck N, Gibson L, Hutchinson J, Wadley H. Metal foams: a design guide. Boston: Butterworth-Heinemann; 2000. [28] Miyoshi T, Itoh M, Akiyama S, Kitahara A. ALPORAS aluminum foam: production process, properties, and applications. Adv Eng Mater 2000;2:179–83.
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Materials and Design journal homepage: www.elsevier.com/locate/matdes
Mechanical behavior improvement of open-pore copper foams synthesized through space holder technique A.M. Parvanian ⇑, M. Panjepour Department of Materials Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran
a r t i c l e
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Article history: Received 3 December 2012 Accepted 29 January 2013 Available online 20 February 2013 Keywords: Open cell metallic foam Lost carbonate sintering Mechanical strength Design of experiments Response surface methodology
a b s t r a c t The use of modern porous materials in different engineering applications necessitates more concentration on open interconnected metallic foams with acceptable mechanical behavior. In this study, openpore copper foams of different porosity percentages with various pore sizes were synthesized through lost carbonate sintering method and then characterized. The effect of copper mechanical pre-activation treatment on flexural strength of the foams was also investigated. The results showed that foams produced by mechanically activated copper powder (350 rpm, 5 h, BPP of 5) have a higher structural integrity, thus enjoying more enhanced mechanical strength relative to specimens without any pre-activation. This may be due to stronger struts mainly resulting from efficient filling of matrix powder between space holder particles. The response surface methodology was also used to examine the effects of carbonate volume percentage and its particle size on the flexural behavior of mechanically optimized foams. Based on the analysis of variances, it was found that the mechanical properties of the foams would improve as a consequence of porosity reduction, while similar relation also exists as average pore sizes decrease. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Porous metallic materials generally known as metal foams have been of increasing interest during recent years due to their unique properties such as high specific strength, heat, electrical conductivity. Based on its openings and connectivity, porosity in metal foams could be divided into closed and open pores. The metallic foams with open interconnected pores are multi-functional, especially for mass and heat transfer applications. For instance, open-pore metallic foams with cell sizes of sub-millimeter were successfully used in fuel cell systems [1,2]. In spite of the numerous methods available for the production of porous metals, only a few are capable of creating open cell foams. In this case, powder metallurgical (PM) processes based on using space holder agent were successfully employed to produce partially open-pore metal foams. Wide range of materials like organic [3,4], inorganic [5] and ceramic particles [6] or even metallic hollow spheres [7] could be used as spacer agent in PM space holder techniques. However, these processes were found to be imperfect. In most cases the mechanical behavior of PM foam products was not very competitive with other more expensive counterparts produced by casting and infiltration methods which are technically very
⇑ Corresponding author. Tel.: +98 311 3912750; fax: +98 311 391 2752. E-mail addresses: [email protected] (A.M. Parvanian), [email protected] (M. Panjepour). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.01.077
expensive and almost suitable for closed-pore foams [8]. In recent years, some research activities were carried out to overcome these shortcomings e.g. by optimization of some process parameters [9,10] or by the introduction of secondary small pores into cell walls [11]. Other activities in this field are devoted to find the relationship between the foam mechanical behavior and some pore network features. Examples include research works done by Wen et al. [12] and similarly by Jiang et al. [13] on the effect of pore size and relative density of some metallic foams on their compressive properties. Others like Goodall et al. [14] have investigated the variation in mechanical response of metallic foams respect to the tortuosity and pore morphology. On the other hand, lots of these cellular structural properties could be controlled by selecting proper parameters in PM method [15,16]. For instance, foam’s porosity percentage, e, and also its average pore diameter, dpore, are closely dependent on the volume percentage of sacrificial space holding material, fc, and its particle size, dc, respectively [17]. So, enhancing the mechanical strength of PM porous products is guaranteed by proper adjusting of process factors. However, it seems that more efforts should be made to improve open cellular metallic foams’ mechanical behavior for high technological applications. The goal of this research work is to manufacture open-pore copper foams by the space holder technique and to understand the effect of matrix powder mechanical pre-activation treatment on the mechanical response of foam products. In the following, the dependency of these metal foams’ mechanical behavior on some intrinsic
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parameters will be studied through a series of designed experiments. 2. Experimental procedure 2.1. Foam synthesis The lost carbonate sintering method patented by Zhao et al. [18] has been used in this research to produce open-cell copper foams. The 99.9% pure commercial copper powder with a particle size of <45 lm was used as matrix phase. As a space holder agent, commercial potassium carbonate powder was sieved into three different powder sizes of 595–841 lm (20 + 30), 420–595 lm (30 + 40), and 297–420 lm (40 + 50) with their corresponding ASTM mesh numbers shown in parentheses. For convenience, this classification was labeled, based on the high levels of ASTM mesh numbers, into 30, 40 and 50, respectively. Different steps of synthesis process are schematically illustrated in Fig. 1. First, the Cu and K2CO3 powders were blended in proper portions with ethanol as binder. In the next step, 30 30 mm2 green compacts were formed under 250 MPa hydraulic pressures. The solid state sintering of the foams was carried out under inert atmosphere preheated to 850 °C for 4 h. Subsequently, space holding carbonate material was thermally decomposed at 1000 °C (2 h). Finally, the specimens were cooled naturally at ambient temperature. In the first step of the experiment, the effect of copper powder pre-activation treatment on the mechanical strength of the foams was investigated. The copper powder was mechanically activated in a planetary ball mill at 350 rpm for about 5 h with balls per powder (BPP) ratio of 5. Fig. 2 depicts the scanning electron microscopy images of pure (Fig. 2a) and mechanically activated (Fig. 2b) copper powders. Afterwards, foams with 70 and 80 vol.% of K2CO3 classified as 50 mesh number, were synthesized and their three-point bending strength, as a criterion of samples’ mechanical behavior, was characterized according to ASTM: E 290. This test was selected as a criterion for the evaluation of mechanical behavior, because the sample in this situation simultaneously encountered compression and tension forces. While selecting proper values for fc and dc through space holder technique could satisfy the manufacturer with the desired e and dpore, the effects of fc and dc factors on flexural properties of foams made of mechanically activated copper were also tried. It was performed by the design of experiments (DOEs) based on central composite design (CCD). First, some screening experiments were performed to choose the appropriate levels to study the factors. For instance, the degree of carbonate loss depended on the sample thickness and decomposition time of specimens with K2CO3 particle sizes smaller than 125 lm [15] which seemed to be reasonable for particles coarser than 250 lm. The collapse of the green bodies with carbonate powders coarser than 800 lm, on the other hand, was more probable [19]. So, the K2CO3 particle size of about 300–800 lm was chosen. Practically, porosities less than about
Fig. 2. SEM micrographs of (a) pure copper powder and (b) after mechanical preactivation treatment (350 rpm, 5 h, BPP of 5).
0.55 resulted in very densely closed foams, while those more than about 0.85 could not provide an acceptable mechanical strength [19]. Therefore, the range of 60–80 porosity percentages was also selected. Finally, fc factor at 60, 70 and 80 levels, and dc with three levels of 30, 40 and 50 were selected for these serial experiments. In spite of full factorial experiments, it is possible to understand the governing relation between the response and the factors more efficiently by the analysis of variances (ANOVA) in CCD resulting from a limited number of experiments. Consequently, the response surface methodology (RSM) could be applied to evaluate the relevance of the mechanical response to selected factors in a wider range. The CCD experimental runs consisting of 22 factorial, four axial, and five center points are shown schematically in Fig. 3. They are also listed in detail in Table 1. For each factor, three levels of 1, 0 and +1 based on their value are coded i.e. low, intermediate, and high, respectively. It is noteworthy to mention that the randomized run order of the experiments considered in this study was to reduce the effects of the factors that were not included; particularly, those effects which were time-dependent. The specimen codes in Table 1 consist of a number after M in which the first two digits demonstrate fc and the second two digits state its corresponding abridged particle size. For the center point runs, the standard order of the specimens is followed at the end of the code. The design and analysis of CCD runs were done by MinitabÒ release 14 software package [15]. 2.2. Characterization The Universal Hounsfield H50KS setup with the loading speed of 1 mm/min was employed in all of the mechanical tests. The flexural strength, rf, of foams could be calculated through Eq. (1) as follows:
Fig. 1. Schematic of lost carbonate sintering process used in this study.
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Fig. 3. Schematic of CCD experimental runs to study the effects of fc and dc on the strength of foams made from mechanically activated copper.
Table 1 Full details of 13 CCD experimental runs.
3. Results and discussion
Standard order
Run order
Specimen code
fc Coded level
dc Coded level
Factorial 1 2 3 4
12 7 4 8
M6030 M6050 M8030 M8050
1 1 +1 +1
1 +1 1 +1
Axial 5 6 7 8
1 2 11 5
M7030 M7050 M6040 M8040
0 0 1 +1
1 +1 0 0
Central 9 10 11 12 13
6 10 9 13 3
M7040-09 M7040-10 M7040-11 M7040-12 M7040-13
0 0 0 0 0
0 0 0 0 0
rf ¼ 3FL=ð2bd2 Þ
3.1. The effect of mechanical pre-activation treatment This section presents the experimental results for the evaluation of foams’ mechanical behavior as a consequence of copper powder pre-activation treatment. The flexural properties of foams produced by powders with and without mechanical activation pretreatment are compared in Fig. 4 as stress–strain curves of samples in two different densities. The dashed lines are related to the foams with no mechanical activation of copper powder (C7050, C8050) and the continuous ones are for samples made of mechanically activated copper (AC7050, AC8050). Similarly, for all of these curves, initial stress grows versus strain with a steep slope. This
ð1Þ
where F is the maximum load before cracking, b is the sample width and d its thickness. The plunge diameter was 3 mm and the span between the two lower supports, L, was selected as 18.5 mm. The flexural modulus of the samples, Ef, can be also calculated using the following equation: 3
Ef ¼ ðmL3 Þ=ð4bd Þ
ð2Þ
where the constant m in the recent equation is the slope of the tangent to the initial straight-line portion of the load–deflection curve. Afterwards, the bulk density of specimens, q, was measured based on ASTM: C20 according to the following equation:
q ¼ W 1 =W 2
ð3Þ
where W1 is dry weight and W2 is the suspended weight of porous specimen in water. Knowing the solid copper matrix theoretical density, qs, was assumed to be 8.94 g cm3 [20], making it possible to calculate e of foam product by the following equation:
e ¼ ð1 q=qs Þ 100
ð4Þ
Scanning Electron Microscopy (SEM) was also used by means of Seron Technology model 550i setup to study the microstructural features of copper foams fracture surfaces. Image analysis of SEM micrographs was performed in OrionÒ image analysis software package.
Fig. 4. Stress–strain curves of foams produced from as received (dashed) and mechanically activated (continuous) copper powder in two different densities.
Table 2 Measurements of mechanical properties and some internal features of samples with and without mechanical pre-activation of copper powder. Sample code
rf (MPa)
Wb
qf (g cm3)
e (%)
rf/qf (MPa/g cm3)
C7050 C8050 AC7050 AC8050
7.2 2.7 22.8 6.6
225.25 105.52 855.61 163.29
2.8 1.9 3.1 2.1
68.7 78.7 65.7 77.2
2.6 1.4 7.4 3.1
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increment continues with a gentle slope. As soon as the flexural force becomes more than the tolerance of porous bodies, the first crack appears and load starts to decrease rapidly as the crack propagates. The mechanical properties of foam samples, rf and bending energy absorption capacity, Wb, i.e. proportional to the underneath area of load–displacement curves in the three-point bending test, are listed in Table 2. Some other characteristics of the porous structures like their q, e and strength to density ratios (rf/qf) are also summarized in this table. The results of C7050 and C8050 are in good agreement with a similar work in the same condition for foam synthesis by spherical copper powder [15]. As summarized in this table and graphically depicted in Fig. 4, the mechanical re-
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sponse of foams has enhanced as a result of mechanical pre-activation of matrix copper powder. This is on average two orders of magnitudes for flexural strength, bending energy absorption capacity and specific flexural strength data. This increment in mechanical load bearing capability of open-pore structures could assure their most modern applications. This phenomenon is more evident for samples with higher densities i.e. those with lower K2CO3 volume percentage. Fig. 5 illustrates microstructure of the samples’ fracture surfaces. In this figure, each specimen cell-wall structure is also depicted in higher magnifications. Generally speaking, the mechanical deformation of porous bodies with porosities more than 0.3 mainly occurs as a consequence of distortion in cell-wall
Fig. 5. SEM micrographs from fracture surfaces of copper foam samples; (a and e) C7050, (b and f) C8050, (c and g) AC7050, and (d and h) AC8050.
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Fig. 6. Schematic illustration of strut strengthening mechanism due to the matrix powder mechanical pre-activation in porous media synthesis process.
regions [21]. Therefore, cell wall thickness would severely influence the mechanical strength of these kinds of materials. The mechanical pre-activation of raw copper powder leads to irregular flake shapes with much more contact areas in which some agglomerations could also occur (Fig. 2). Naturally, the flake morphologies have higher compressibility and sintering efficiency than other particle shapes [22]. Fig. 6 schematically shows the porous media synthesis process. This morphological change can severely reduce the number of micropores during compaction step, shown as white arrows in Fig. 5e and f, resulting in stronger mechanical bonding between matrix particles. Thus, merging of flake copper particles eventuates in a more efficient solid state sintering process. This could form denser struts with more continuity of the solid skeleton or stronger necks to withstand mechanical stresses several orders of magnitudes. The denser the foam sample, the more efficient the strut strengthening is.
Fig. 7. Main effects of fc and dc on the porosity (top) and average pore size (bottom) of copper foams.
Table 4 ANOVA of full quadratic regression model for flexural strength data. Source
d.f.
Seq. SS
Adj. SS
Adj. MS
f
p
fc dc fc fc dc dc fc dc Error Total
1 1 1 1 1 7 12
1008.29 9.33 0.00 0.02 8.97 148.40 1175.00
1008.29 9.33 0.00 0.02 8.97 148.40
1008.29 9.33 0.00 0.02 8.97 21.20
47.56 0.44 0.00 0.00 0.42
0.000 0.528 0.999 0.979 0.536
3.2. Response surface methodology (RSM) The experimental results of CCD runs investigating the effects of some pore network features on mechanical response of foams produced from mechanically activated copper powder are discussed in
this section. Table 3 summarizes measurements of these foams’ internal features and also their mechanical strength data. The ANOVA as a reliable tool could be used to understand the meaningful
Table 3 Measurements of foams’ internal features and their mechanical properties. Standard order
Specimen code
qf (g cm3)
e (%)
dpore (lm)
rf (MPa)
rf/qf (MPa cm3 g1)
1 2 3 4 5 6 7 8 9 10 11 12 13
M6030 M6050 M8030 M8050 M7030 M7050 M6040 M8040 M7040-09 M7040-10 M7040-11 M7040-12 M7040-13
3.3 3.2 2.1 2 2.5 3.1 3.4 2 2.5 2.8 2.8 3.1 2.7
62.9 63.8 76.5 77.2 72.3 65.7 62.3 77.3 71.5 69.1 68.5 65.3 69.6
619 ± 22 401 ± 17 622 ± 9 384 ± 21 623 ± 23 380 ± 23 529 ± 23 509 ± 10 542 ± 11 500 ± 15 477 ± 23 529 ± 8 453 ± 10
26.93 33.16 6.57 6.81 23.85 24.86 39.97 8.9 15.48 22.84 18.55 16.8 20.52
8.2 10.4 3.1 3.4 9.5 8.0 11.8 4.5 6.2 8.2 6.6 5.4 7.6
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Fig. 8. Residual plots for flexural strength statistical analysis as (a) normal probability distribution; (b) histogram; (c) residuals versus fits; and (d) residuals versus order.
Table 5 Fitted regression models on flexural strength data with each R square values. Model
R2
R2adj:
R2predict:
Linear Linear + squares Linear + interaction Full quadratic
86.61 86.61 87.37 87.37
83.93 79.91 83.16 78.35
75.73 55.22 66.23 23.42
Table 7 Linear regression model coefficients. Term
Coefficient
S.E. Coef.
t Value
p Value
Constant fc dc
20.403 12.963 1.249
1.100 1.620 1.620
18.453 8.004 0.770
0.000 0.000 0.459
S = 3.96722, R2 = 86.61%, R2adj: ¼ 83:93%, R2predict: ¼ 75:73.
Table 6 ANOVA of linear regression model fitted on flexural strength data. Source
DF
Seq. SS
Adj. SS
Adj. MS
f Value
p Value
fc dc Residual error Total
1 1 10 12
1008.29 9.33 157.39 1175.00
1008.29 9.33 157.39
1008.29 9.33 15.74
64.06 0.59
0.000 0.459
effects of synthesis parameters i.e. fc and dc on these data. Indeed, ANOVA was applied to test the null hypothesis with respect to the data acquired during designed experimentations. Through null hypothesis it is assumed that there is no difference in treatment means (H0:l1 = l1 = = la). The ANOVA results are plotted in Fig. 7 as the main effects of fc and dc on some geometrical features of foams, i.e. their e and dpore. By comparing the slopes of the lines, one can compare the relative magnitudes of the effects of each factor. Apparently, fc could induce the main influential effect on samples’ e and dc as well as on foams’ dpore, while the effect of the complementary factor in each case is negligible; regarding the fact that increasing ASTM mesh number
Fig. 9. The RSM of flexural strength values vs. fc and dc.
of carbonate powder, which means the decrement of dc, equally decreases samples’ dpore. Actually, these analyses can properly de-
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Fig. 10. The contour plot of flexural strength values vs. fc and dc.
scribe the dependency of e and dpore of the porous structures produced via space holder techniques on the volume percentage, fc, and particle size, dc, of sacrificial agent, respectively. This is why this method could be used for the synthesis of porous structures with desired e and dpore. In the following, regression statistical analysis of flexural strength data (Table 3) is performed and the results are presented as ANOVA calculations with full quadratic terms of fc and dc in Table 4. It is noteworthy to mention that all ANOVA calculations in this study have been done using coded units of 1, 0 and +1 for low, intermediate and high levels for each factor, respectively. The corresponding residual plots are also illustrated in Fig. 8. The normality of residuals could be understood from the straight line distribution as shown in Fig. 8a. The bell-shaped histogram plot in Fig. 8b also confirms the error normality assumption. The scattered distribution of dots with no structure above and below the abscissa (fitted values) in Fig. 8c and d proves both the error independency and variance constancy [23]. Generally, regression coefficients with p values less than the confidence interval of 0.05 would have more significant changes on the response. As seen from Table 4, term fc that was proved before as the main controlling factor of foams’ e, is the most significant coefficient in this regression model. In any case, other models including linearity with and without interaction or square terms of factors should be checked to find the best fitted model. The fitted R2 values of other regression analyses are listed in Table 5.
According to Table 5, the values of R2 and R2adj: indicate the goodness of the model to fit the data, while R2predict: shows how well the model predicts responses to new observations. Actually, the recent parameter can prevent over-fitting of the model and could be more useful than R2adj: to compare the models, because it is calculated by the use of observations which are not included in the model estimation [24]. As this table suggests, linear regression model is the best with the highest R2adj: and R2predict: values to predict foams’ flexural response. The R2 value also indicates that the predictors explain 86.61% of the variances for flexural strengths in this regression model. The linear regression model can be the most reliable to predict the flexural strength data. The ANOVA results for this model are also summarized in Table 6. The coefficients of factors and factor effects of this model, analyzed by coded units, are also listed in Table 7. Regularly, for a confidence level of 95%, dc does not show any effect as much significant as fc, but as a main factor it may be helpful to study it more in detail by means of response surface methodology. Fig. 9 depicts the RSM of flexural strengths as a linear function of fc and dc. The projected contours on the factor’s plane, as shown in Fig. 10, suggests a minor improvement of copper foams’ mechanical behavior with a decrement of fc and an increment of dc which means a decrease in e and dpore. In this regard, the effect of e on the mechanical behavior of foams seems to be in good agreement with other similar works [13,16,21,25,26]. The power relationship between Young’s modulus of a cellular structure, E, and its relative density, q/qs, reported by Gibson and Ashby [21], may be the most applicable one known as GA model (Eq. (5)).
E=Es ¼ Cðq=qs Þ2 ¼ Cð1 eÞ2
ð5Þ
where Es is Young’s modulus of solid matrix and is assumed to be around 170 GPa for copper matrix; C and n are also geometric constants of proportionality. The value of C was suggested to be within the range of 0.1–4 for idealized open cellular structures under compression forces [21]. In the case of porous samples’ flexural modulus, an equation similar to Eq. (5) could be also assumed [27]. The relative flexural modulus of synthesized copper foams, Ef/Es, versus their densities, q/qs, are plotted in Fig. 11. A power regression equation with C = 0.0173 and n 1.9 was also fitted on this curve with R2 80%. Through pressurizing the powder mixture in LCS process, the space holder particles tend to glide on each other and rearrange preferentially along their elongated sides. This could result in a nonisotropic foam with irregular pore structure. As cited before, Eq. (5)
Fig. 11. Relative flexural modulus vs. relative density of copper foam products.
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has been introduced for open-pore metallic foams with a regular pattern of pore structure. So, the minor differences between the fitted equation and GA model may refer to the irregularity or nonhomogeneity of pore structure in copper foam products which may results in cell walls even without any contribution to load bearing. Despite the effects of e or relative density on mechanical properties of copper foams, there are some contradictories associated with their dpore which could be controlled closely by dc. Using a simple model for porous metallic foams failure, Gibson and Ashby [21] found no relation between the collapse stress and pore size. Tao et al. [16] reported higher rf and Wb for porous copper samples produced by LCS with coarser carbonate powder. The spacious interstices between larger K2CO3 particles surrounded by the spherical Cu powder, were stated as the main reason for stronger cell wall structure. However, it was also suggested that this size difference effect should be insignificant for K2CO3–copper particle size ratio of greater than five. Jiang et al. [13] also discovered an increase in compressive stress–strain curves of Al foams due to an increment of carbamide sacrificial particles ranging from 0.45 to 2 mm. As another finding, improvement of reproducibility and predictability of compressive properties and control precision of relative density due to dpore increase were noticed in this work and also in [25]. On the other hand, some researchers reported higher mechanical strength for the porous metallic materials with smaller dpore [12,28]. Changes in aspect ratio of the cell wall thickness against its edge length has been stated as one of the most promising reasons for this phenomenon [28]. Anyway, the mechanical pre-activation treatment of copper powder performed in this study led to the finer flake particles which could form a thin cover around K2CO3 spheres which completes the filling of interstitial spaces between space holder particles and can minimize the defects in cell wall region mentioned in [16]. In other words, as discussed before, more efficient sintering process could be achieved due to this change in matrix powder morphology. These enhancements would form ligaments with better structural integrity and with stronger cell walls to withstand mechanical loadings. Somehow, as illustrated in Figs. 9 and 10, this strength improvement is more significant for the foams with smaller dpore. In fact, pore size decrement as a consequence of increasing carbonate ASTM mesh number in this study, may increase the density of stronger ligaments i.e. the number of struts in a definite volume, which might improve porous structure mechanical response. 4. Conclusions Synthesis and development of open-pore copper foams through LCS method were investigated in this study. The results show that space holder techniques like LCS could accurately control the e and dpore of the final foam products. It was found that mechanical preactivation of copper powder, and thus changing its morphology could enhance the structural integrity of foams and thus their mechanical strength at least two orders of magnitudes. This was noticeable in foams with higher densities. A series of designed experimental runs on these mechanically enhanced foams also revealed that increasing carbonate volume percentage and equally increasing e could rigorously influence flexural strength of specimens through a power relation similar to GA model. It was also found that decreasing dpore resulted in better mechanical responses, which is mainly due to more integrated struts in a definite volume of the foams with smaller dpore produced by mechanically activated copper powder. However, more thorough study may be needed to investigate this effect in a wider range of particle sizes.
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